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    "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2018  by D. Koehn, notebook style sheet by L.A. Barba, N.C. Clementi"
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    "# Execute this cell to load the notebook's style sheet, then ignore it\n",
    "from IPython.core.display import HTML\n",
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    "HTML(open(css_file, \"r\").read())"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical stability, dispersion and anisotropy of the 2D acoustic finite difference modelling code\n",
    "\n",
    "Similar to the 1D acoustic FD modelling code, we have to investigate the stability and dispersion of the 2D numerical scheme. Additionally, the numerical dispersion shows in the 2D case an anisotropic behaviour.\n",
    "\n",
    "Let's begin with the CFL-stability criterion ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CFL-stability criterion for the 2D acoustic FD modelling code\n",
    "\n",
    "As for the 1D code, the maximum size of the timestep $dt$ is limited by the Courant-Friedrichs-Lewy (CFL) criterion:\n",
    "\n",
    "\\begin{equation}\n",
    "dt \\le \\frac{dx}{\\zeta v_{max}}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "where $dx$ denotes the spatial grid point distance and $v_{max}$ the maximum P-wave velocity. The factor $\\zeta$ depends on the used FD-operators, dimension and numerical scheme.\n",
    "\n",
    "As for the [1D case](http://nbviewer.jupyter.org/github/daniel-koehn/Theory-of-seismic-waves-II/blob/master/04_FD_stability_dispersion/1_fd_stability_dispersion.ipynb), we estimate the factor $\\zeta$ by the von Neumann analysis, starting with the finite difference approximation of the 2D acoustic wave equation\n",
    "\n",
    "\\begin{equation}\n",
    " \\frac{p_{j,l}^{n+1} - 2 p_{j,l}^n + p_{j,l}^{n-1}}{\\mathrm{d}t^2} \\ = \\ vp_{j,l}^2\\biggl(\\frac{p_{j,l+1}^{n} - 2 p_{j,l}^n + p_{j,l-1}^{n}}{\\mathrm{d}x^2} + \\frac{p_{j+1,l}^{n} - 2 p_{j,l}^n + p_{j-1,l}^{n}}{\\mathrm{d}z^2}\\biggr),\n",
    "\\end{equation}\n",
    "\n",
    "and assuming harmonic plane wave solutions for the pressure wavefield of the form:\n",
    "\n",
    "\\begin{equation}\n",
    "p = exp(i(k_x x + k_z z -\\omega t)),\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "with $i^2=-1$, the wavenumbers $(k_x, k_z)$ in x-/z-direction, respectively, and the circular frequency $\\omega$. Using a regular grid with \n",
    "\n",
    "$dx = dz = dh,$\n",
    "\n",
    "discrete spatial coordinates  \n",
    "\n",
    "$x_j = j dh,$\n",
    "\n",
    "$z_l = l dh,$\n",
    "\n",
    "and times \n",
    "\n",
    "$t_n = n dt.$\n",
    "\n",
    "we can calculate discrete plane wave solutions at the discrete locations and times in eq. (1):  \n",
    "\n",
    "\\begin{align}\n",
    "p_{j,l}^{n+1} &= exp(-i\\omega dt)\\; p_{j,l}^{n},\\\\\n",
    "p_{j,l}^{n-1} &= exp(i\\omega dt)\\; p_{j,l}^{n},\\\\\n",
    "p_{j+1,l}^{n} &= exp(ik_x dh)\\; p_{j,l}^{n},\\\\\n",
    "p_{j-1,l}^{n} &= exp(-ik_x dh)\\; p_{j,l}^{n},\\\\\n",
    "p_{j,l+1}^{n} &= exp(ik_z dh)\\; p_{j,l}^{n},\\\\\n",
    "p_{j,l-1}^{n} &= exp(-ik_z dh)\\; p_{j,l}^{n},\\\\\n",
    "\\end{align}\n",
    "\n",
    "Inserting eqs. (2) - (7) into eq. (1), division by $p_{j,l}^{n}$ and using the definition: \n",
    "\n",
    "\\begin{equation}\n",
    "\\cos(x) = \\frac{exp(ix) + exp(-ix)}{2},\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "yields:\n",
    "\n",
    "\\begin{equation}\n",
    "cos(\\omega dt) - 1 = vp_{j,l}^2 \\frac{dt^2}{dh^2}\\biggl(\\{cos(k_x dh) - 1\\} + \\{cos(k_z dh) - 1\\}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Some further rearrangements and division of both sides by 2, leads to:\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1 - cos(\\omega dt)}{2} = vp_{j,l}^2 \\frac{dt^2}{dh^2}\\biggl(\\frac{1 - cos(k_x dh)}{2} + \\frac{1 - cos(k_z dh)}{2}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "With the relation \n",
    "\n",
    "\\begin{equation}\n",
    "sin^2\\biggl(\\frac{x}{2}\\biggr) = \\frac{1-cos(x)}{2}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "we get \n",
    "\n",
    "\\begin{equation}\n",
    "sin^2\\biggl(\\frac{\\omega dt}{2}\\biggr) = vp_{j,l}^2 \\frac{dt^2}{dh^2}\\biggl(sin^2\\biggl(\\frac{k_x dh}{2}\\biggr)+sin^2\\biggl(\\frac{k_z dh}{2}\\biggr)\\biggr). \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Taking the square root of both sides finally yields \n",
    "\n",
    "\\begin{equation}\n",
    "sin\\biggl(\\frac{\\omega dt}{2}\\biggr) = vp_{j,l} \\frac{dt}{dh}\\sqrt{sin^2\\biggl(\\frac{k_x dh}{2}\\biggr)+sin^2\\biggl(\\frac{k_z dh}{2}\\biggr)}.\n",
    "\\end{equation}\n",
    "\n",
    "This result implies, that if the Courant number\n",
    "\n",
    "\\begin{equation}\n",
    "\\epsilon = vp_{j,l} \\frac{dt}{dh} \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "is larger than $1/\\sqrt{2}$, you get only imaginary solutions, while the real part is zero (think for a second why). Consequently, the numerical scheme becomes unstable, when the following CFL-criterion is violated\n",
    "\n",
    "\\begin{equation}\n",
    "\\epsilon = vp_{j,l} \\frac{dt}{dh} \\le \\frac{1}{\\sqrt{2}} \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Rearrangement to the time step dt, assuming that we have defined a spatial grid point distance dh and replacing $vp_{j,l}$ by the maximum P-wave velocity in the FD model $v_{max}$, leads to \n",
    "\n",
    "\\begin{equation}\n",
    "dt  \\le \\frac{dh}{\\sqrt{2}v_{max}}. \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Therefore, the factor $\\zeta$ in the general CFL-criterion\n",
    "\n",
    "\\begin{equation}\n",
    "dt  \\le \\frac{dh}{\\zeta vp_j}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "for the FD solution of the 2D acoustic wave equation using the temporal/spatial 3-point operator to approximate the 2nd derivative is $\\zeta = \\sqrt{2}$. \n",
    "\n",
    "Let's check if this result ist correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0
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   "outputs": [],
   "source": [
    "# Import Libraries \n",
    "# ----------------\n",
    "import numpy as np\n",
    "from numba import jit\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import rcParams\n",
    "\n",
    "# Ignore Warning Messages\n",
    "# -----------------------\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": [],
    "scrolled": false
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   "outputs": [],
   "source": [
    "# Definition of modelling parameters\n",
    "# ----------------------------------\n",
    "xmax = 5000.0 # maximum spatial extension of the 1D model in x-direction (m)\n",
    "zmax = xmax   # maximum spatial extension of the 1D model in z-direction (m)\n",
    "dx   = 10.0   # grid point distance in x-direction (m)\n",
    "dz   = dx     # grid point distance in z-direction (m)\n",
    "\n",
    "tmax = 0.8    # maximum recording time of the seismogram (s)\n",
    "dt   = 0.0010 # time step\n",
    "\n",
    "vp0  = 3000.  # P-wave speed in medium (m/s)\n",
    "\n",
    "# acquisition geometry\n",
    "xr = 2000.0   # x-receiver position (m)\n",
    "zr = xr       # z-receiver position (m)\n",
    "\n",
    "xsrc = 2500.0 # x-source position (m)\n",
    "zsrc = xsrc   # z-source position (m)\n",
    "\n",
    "f0   = 20. # dominant frequency of the source (Hz)\n",
    "t0   = 4. / f0 # source time shift (s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FD_2D_acoustic code with JIT optimization\n",
    "# -----------------------------------------\n",
    "@jit(nopython=True) # use Just-In-Time (JIT) Compilation for C-performance\n",
    "def FD_2D_acoustic_JIT(dt,dx,dz,f0):        \n",
    "    \n",
    "    # define model discretization\n",
    "    # ---------------------------\n",
    "\n",
    "    nx = (int)(xmax/dx) # number of grid points in x-direction\n",
    "    print('nx = ',nx)\n",
    "\n",
    "    nz = (int)(zmax/dz) # number of grid points in x-direction\n",
    "    print('nz = ',nz)\n",
    "\n",
    "    nt = (int)(tmax/dt) # maximum number of time steps            \n",
    "    print('nt = ',nt)\n",
    "\n",
    "    ir = (int)(xr/dx)      # receiver location in grid in x-direction    \n",
    "    jr = (int)(zr/dz)      # receiver location in grid in z-direction\n",
    "\n",
    "    isrc = (int)(xsrc/dx)  # source location in grid in x-direction\n",
    "    jsrc = (int)(zsrc/dz)  # source location in grid in x-direction\n",
    "\n",
    "    # Source time function (Gaussian)\n",
    "    # -------------------------------\n",
    "    src  = np.zeros(nt + 1)\n",
    "    time = np.linspace(0 * dt, nt * dt, nt)\n",
    "\n",
    "    # 1st derivative of a Gaussian\n",
    "    src  = -2. * (time - t0) * (f0 ** 2) * (np.exp(- (f0 ** 2) * (time - t0) ** 2))\n",
    "        \n",
    "    # Analytical solution\n",
    "    # -------------------\n",
    "    G    = time * 0.\n",
    "\n",
    "    # Initialize coordinates\n",
    "    # ----------------------\n",
    "    x    = np.arange(nx)\n",
    "    x    = x * dx       # coordinates in x-direction (m)\n",
    "\n",
    "    z    = np.arange(nz)\n",
    "    z    = z * dz       # coordinates in z-direction (m)\n",
    "\n",
    "    # calculate source-receiver distance\n",
    "    r = np.sqrt((x[ir] - x[isrc])**2 + (z[jr] - z[jsrc])**2)\n",
    "\n",
    "    for it in range(nt): # Calculate Green's function (Heaviside function)\n",
    "        if (time[it] - r / vp0) >= 0:\n",
    "            G[it] = 1. / (2 * np.pi * vp0**2) * (1. / np.sqrt(time[it]**2 - (r/vp0)**2))\n",
    "    Gc   = np.convolve(G, src * dt)\n",
    "    Gc   = Gc[0:nt]\n",
    "\n",
    "    # Initialize model (assume homogeneous model)\n",
    "    # -------------------------------------------\n",
    "    vp    = np.zeros((nx,nz))\n",
    "    vp2    = np.zeros((nx,nz))\n",
    "\n",
    "    vp  = vp + vp0       # initialize wave velocity in model\n",
    "    vp2 = vp**2\n",
    "    \n",
    "    # Initialize empty pressure arrays\n",
    "    # --------------------------------\n",
    "    p    = np.zeros((nx,nz)) # p at time n (now)\n",
    "    pold = np.zeros((nx,nz)) # p at time n-1 (past)\n",
    "    pnew = np.zeros((nx,nz)) # p at time n+1 (present)\n",
    "    d2px = np.zeros((nx,nz)) # 2nd spatial x-derivative of p\n",
    "    d2pz = np.zeros((nx,nz)) # 2nd spatial z-derivative of p\n",
    "\n",
    "    # Initialize empty seismogram\n",
    "    # ---------------------------\n",
    "    seis = np.zeros(nt) \n",
    "    \n",
    "    # Calculate Partial Derivatives\n",
    "    # -----------------------------\n",
    "    for it in range(nt):\n",
    "    \n",
    "        # FD approximation of spatial derivative by 3 point operator\n",
    "        for i in range(1, nx - 1):\n",
    "            for j in range(1, nz - 1):\n",
    "                \n",
    "                d2px[i,j] = (p[i + 1,j] - 2 * p[i,j] + p[i - 1,j]) / dx**2                \n",
    "                d2pz[i,j] = (p[i,j + 1] - 2 * p[i,j] + p[i,j - 1]) / dz**2\n",
    "\n",
    "        # Time Extrapolation\n",
    "        # ------------------\n",
    "        pnew = 2 * p - pold + vp2 * dt**2 * (d2px + d2pz)\n",
    "\n",
    "        # Add Source Term at isrc\n",
    "        # -----------------------\n",
    "        # Absolute pressure w.r.t analytical solution\n",
    "        pnew[isrc,jsrc] = pnew[isrc,jsrc] + src[it] / (dx * dz) * dt ** 2\n",
    "                \n",
    "        # Remap Time Levels\n",
    "        # -----------------\n",
    "        pold, p = p, pnew\n",
    "    \n",
    "        # Output of Seismogram\n",
    "        # -----------------\n",
    "        seis[it] = p[ir,jr]        \n",
    "        \n",
    "    return time, seis, Gc, p     # return last pressure wave field snapshot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To seperate modelling and visualization of the results, we introduce the following plotting function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compare FD Seismogram with analytical solution\n",
    "# ---------------------------------------------- \n",
    "def plot_seis(time,seis_FD,seis_analy):     \n",
    "    \n",
    "    # Define figure size\n",
    "    rcParams['figure.figsize'] = 12, 5\n",
    "    \n",
    "    plt.plot(time, seis_FD, 'b-',lw=3,label=\"FD solution\") # plot FD seismogram\n",
    "    plt.plot(time, seis_analy,'r--',lw=3,label=\"Analytical solution\") # plot analytical solution\n",
    "    \n",
    "    plt.xlim(time[0], time[-1])\n",
    "    \n",
    "    plt.title('Seismogram')\n",
    "    plt.xlabel('Time (s)')\n",
    "    plt.ylabel('Amplitude')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    \n",
    "    plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  500\n",
      "nz =  500\n",
      "nt =  339\n",
      "CPU times: user 2.21 s, sys: 12 ms, total: 2.22 s\n",
      "Wall time: 2.22 s\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx   = 10.0   # grid point distance in x-direction (m)\n",
    "dz   = dx     # grid point distance in z-direction (m)\n",
    "f0   = 20     # centre frequency of the source wavelet (Hz)\n",
    "\n",
    "# define \n",
    "zeta = np.sqrt(2)\n",
    "\n",
    "# calculate dt according to the CFL-criterion\n",
    "dt = dx / (zeta * vp0)\n",
    "\n",
    "%time time, seis_FD, seis_analy, p = FD_2D_acoustic_JIT(dt,dx,dz,f0)\n",
    "plot_seis(time,seis_FD,seis_analy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical Grid Dispersion\n",
    "\n",
    "While the FD solution above is stable, it is subject to some numerical dispersion when compared with the analytical solution. The grid point distance $dx = 10\\; m$, P-wave velocity $vp = 3000\\; m/s$ and a maximum frequency $f_{max} \\approx 2*f_0 = 40\\; Hz$ leads to ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N_lam =  7.5\n"
     ]
    }
   ],
   "source": [
    "fmax = 2 * f0 \n",
    "N_lam = vp0 / (dx * fmax)\n",
    "print(\"N_lam = \",N_lam)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$N_\\lambda = 7.5$ gridpoints per minimum wavelength. Let's increase it to $N_\\lambda = 12$, which yields ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  800\n",
      "nz =  800\n",
      "nt =  543\n",
      "CPU times: user 1.83 s, sys: 12 ms, total: 1.84 s\n",
      "Wall time: 1.83 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_lam = 12 \n",
    "dx   = vp0 / (N_lam * fmax)\n",
    "dz   = dx     # grid point distance in z-direction (m)\n",
    "f0   = 20     # centre frequency of the source wavelet (Hz)\n",
    "\n",
    "# define \n",
    "zeta = np.sqrt(2)\n",
    "\n",
    "# calculate dt according to the CFL-criterion\n",
    "dt = dx / (zeta * vp0)\n",
    "\n",
    "%time time, seis_FD, seis_analy, p = FD_2D_acoustic_JIT(dt,dx,dz,f0)\n",
    "plot_seis(time,seis_FD,seis_analy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... an improved fit of the 2D analytical by the FD solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical Anisotropy\n",
    "\n",
    "Compared to the 1D acoustic case, the numerical dispersion behaves a little bit differently in the 2D FD approximation. To illustrate this problem, we model the pressure wavefield for $t_{max} = 0.8\\; s$for a fixed grid point distance of $dx = 10\\;m$ and a centre frequency of the source wavelet $f0 = 100\\; Hz$ which corresonds to $N_\\lambda = 1.5$ grid points per minimum wavelength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  500\n",
      "nz =  500\n",
      "nt =  339\n"
     ]
    }
   ],
   "source": [
    "# define dx/dz and calculate dt according to the CFL-criterion\n",
    "dx   = 10.0   # grid point distance in x-direction (m)\n",
    "dz   = dx     # grid point distance in z-direction (m)\n",
    "# define zeta for the CFL criterion\n",
    "zeta = np.sqrt(2)\n",
    "dt = dx / (zeta * vp0)\n",
    "\n",
    "f0 = 100\n",
    "time, seis_FD, seis_analy, p = FD_2D_acoustic_JIT(dt,dx,dz,f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot last pressure wavefield snapshot at Tmax = 0.8 s\n",
    "# -----------------------------------------------------\n",
    "rcParams['figure.figsize'] = 8, 8 # define figure size\n",
    "\n",
    "clip = 1e-7  # image clipping\n",
    "extent = [0.0, xmax/1000, 0.0, zmax/1000]\n",
    "\n",
    "# Plot wavefield snapshot at tmax = 0.8 s\n",
    "plt.imshow(p.T,interpolation='none',cmap='seismic',vmin=-clip,vmax=clip,extent=extent)\n",
    "plt.title('Numerical anisotropy')\n",
    "plt.xlabel('x (km)')\n",
    "plt.ylabel('z (km)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, a spatial discretization with $N_\\lambda = 1.5$ gridpoints per minimum wavelength leads to modelling results significantly affected by dispersion. However, note that the dispersion is direction dependent. Maximum dispersion coincides with the main Cartesian coordinate axes, while the dispersion reaches a minimum at 45° angles relative to the main axes. This problem is called **Numerical Anisotropy** and can be explained by the angle dependence of the numerical phase velocity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What we learned:\n",
    "\n",
    "* Estimation of the CFL-criterion for the FD approximation of the 2D acoustic wave equation using von Neumann analysis\n",
    "* Verification of CFL and grid dispersion criterion by 2D numerical FD modelling\n",
    "* Be aware of the influence of numerical anisotropy on FD modelling results"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
